November 20, 2009
Robert Rodini is literally immersed in mathematics. He not only studies it, he lives it. So, although he's quite respected as a problem solving software engineer, he's now returned to university, 40 years after getting his bachelor's degree in math. He's looking at a second career as a mathematician and is particularly passionate about number theory and abstract algebra. While most people, with many exceptions, struggle with math, Rodini says he agrees with Karl Gauss, the 19th century German mathematician, who said that "number theory is the queen of mathematics." Of course!
I believe in mathematics.
I believe this not because I'm great at math, but because the subject inspires me. It inspired me as an undergraduate 40 years ago, and it inspires me anew as a graduate student. It will continue to inspire me in the future when I begin a second career as a mathematics teacher.
Why believe in math? Well, besides being essential to science and technology, which are keys to our modern society, mathematics teaches many important values.
I believe math teaches you to be open-minded.
In the nineteenth century mathematicians realized the possibility of non-Euclidean geometries that are just as valid as the Euclidean geometry we learned in high school. And in the twentieth century astrophysicists proved the true nature of our universe to be non-Euclidean. How wrong-headed would it have been to have stuck only with Euclid?
I claim that math teaches humility because in 1931 a meta-mathematician named Kurt Goedel proved that there are limits to formal systems that mathematicians just cannot overcome by their ingenuity. This is not the "I'm not good at math" type of limitation; it's the "incompleteness" of the mathematical system itself. This incompleteness is beyond repair by the human intellect - quite a humbling notion, indeed.
Math also teaches you to avoid false generalizations as there are patterns that are true for the first million, million instances, but then fail to be true beyond that point. How quick are we to affirm stereotypes based on a just a few experiences? Mathematicians strive to avoid false generalizations knowing that their conclusions must rely on rigorous proofs.
I believe that math teaches perseverance of an extraordinary degree. In the seventeen hundreds Pierre Fermat postulated his "last theorem." It wasn't a theorem at all since Fermat had not proved it; however, for the next 300 years every number theorist worth his salt took a crack at the proof. They all met with failure, that is, until Andrew Wiles proved the theorem in 1995 at Princeton University.
Now on a personal level math has taught me humility. What other subject can make you feel like an idiot than this one? Others might say that "Bob's just good at math," but I know the determination and perseverance it takes to finish a problem set, to agonize over an exam, to grind through a course, and to accept a final grade. I know why some people hate math, but that's just it - there's value in the struggle.
What can you learn from studying math besides equations and formulas? Well, it trains your mind in a wonderful way to process and synthesize information and to apply that information to the problem at hand. Isn't that useful in everyday life?
I believe in mathematics for its beauty and truth, and for the values it teaches.